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A rainstorm increased the amount of water stored in State J

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A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44

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[Reveal] Spoiler: OA

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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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SOLUTION

A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44

Since we need to find only an approximate value and the answer choices are quite widespread, then use:

80% instead of 82% (notice that this approximation gives the bigger tank capacity);
140 billion gallons instead of 138 billion gallons (notice that this approximation also gives the bigger tank capacity);
130 billion gallons instead of 124 billion gallons;.

Notice that the third approximation balances the first two a little bit.

So, we'll have that: \(capacity*0.8=140\) --> \(capacity=\frac{140}{0.8}=175\).

Hence, the amount of water the reservoirs were short of total capacity prior to the storm was approximately \(175-130=45\) billion gallons.

Answer: E.
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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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New post 30 Jul 2012, 01:25
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Currently 138 billion which is 82% of capacity.
i.e.
Capacity*82%= 138 billion
Capacity=\(\frac{138}{82%}\)
Capacity=168.3 billion

Thus it was short of 168.3-124= 44 billion gallons

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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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Bunuel wrote:
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44

Practice Questions
Question: 6
Page: 152
Difficulty: 600



Since an approximation is needed, and we cannot use a calculator, I would take that 138 billion represents only 80 percent of the full capacity. I know that my answer will be a slight overshoot. So, if 138 is 80%, then 10% is 138/8 = 34.5/2 = 17.25, and 100% will be 172.5 billion. My overshot answer is 172.5-124=48.5.
So, the correct answer should be 44.
Just to be on the safe side: (124+30)*0.8=154*0.8=123.2 and (124+44)*0.8=168*0.8= 134.4, so definitely, 44 is the correct answer.

By a second thought, if we think of "ball parking", then all we need are the last two tests above. It is clear that the answer should be greater than 14 (124+14=138, which is just 82% of full capacity). No need to calculate the full capacity and then the required difference, it is sufficient to check that (124 + the answer) * 0.8 is the closest to 138.

Not a pretty question...

Answer E
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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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New post 17 Jan 2014, 03:31
Calculation approach:

1 % of capacity equals: 138/82 = 1.7 (rounded)gal (since 0.7*82 is slightly greater than 138). 100% of capacity = 100*1.7 = 170 = full capacity of tank.

170-124= 46 which is very close to E. Hence E.

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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

Solution:

82% * Cap =138
Cap = (138*100)/82
Using approximation:
Cap = (136*100)/80

Note: Den and Num decreased, Hence both cancel out each others effect.

Cap =136*(5/4) = 34*5 = 170

Now, 170-124 = 46 = ~44 (Nearest answer)

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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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82% capacity = 138 Billion Gallons, so 100% =

\(138 * \frac{100}{82} = \frac{6900}{41}\)

Shortfall before rain =

\(\frac{6900}{41} - 124\)

\(= \frac{1816}{41}\)

= 44 (Approx)

Answer = E
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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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New post 31 May 2014, 11:14
After the reservoir is filled to 138 gallons the amount of water is at 82% or roughly 80% - which means that 20% of the reservoir is empty. To figure out what that 20% is approximate: 140 gallons /80 percent = x gallons /20 percent , therefore, x = 35 gallons , answer choices A,B,C,D are below 35 . We know that the reservoir must be short more than 35 gallons, therefore, the only possible choice is E.



Thinking about this question visually you see that the # of gallons that the reservoir was originally short = different b/w 138 & 124 + difference b/w total & 138
(138 gallons - 124 gallons) + (total gallons - 138 gallons)

Eliminate A & B, because the difference b/w 138 & 124 = 14, and after filling up to 138 gallons there is still 18% of space left in the reservoir. Knowing this we know that the answer choice has to be higher than 14 gallons. To figure out how much higher approximate:

138% = 82% we can derive that approximately 140 gallons = 80% ; remaining 20% = 140 * 20/80 = 35 gallons even without doing the calculation any further you can eliminate answer choices C & D because 35 gallons is higher than both C & D.

14 + 35 = 49 gallons

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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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New post 09 Sep 2014, 10:10
Bunuel wrote:
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44

Practice Questions
Question: 6
Page: 152
Difficulty: 600


clumsy numbers in the problem..

138 is 82% of total. then total = (138*100)/82 = appro 168

before the storm it was 124 then 168-124 = 44

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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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New post 17 Mar 2015, 05:40
Bunuel wrote:
SOLUTION

A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44

Since we need to find only an approximate value and the answer choices are quite widespread, then use:

80% instead of 82% (notice that this approximation gives the bigger tank capacity);
140 billion gallons instead of 138 billion gallons (notice that this approximation also gives the bigger tank capacity);
130 billion gallons instead of 124 billion gallons;.

Notice that the third approximation balances the first two a little bit.

So, we'll have that: \(capacity*0.8=140\) --> \(capacity=\frac{140}{0.8}=175\).

Hence, the amount of water the reservoirs were short of total capacity prior to the storm was approximately \(175-130=45\) billion gallons.

Answer: E.

This is my first post on a question, but this question makes me feel really ignorant. I understand most of the concept for finding the answer, but my general math is not strong. When I see \((140/0.8)\), I feel like that is starting to get math heavy and don't have the skills to handle that in my head. Perhaps there is a concept you can point me too to help manipulate such a fraction in my head or another solution not calculation intensive?
I feel just as ignorant when I see \(138/82%\), otherwise I get how to solve the problem. Please forgive my ignorance, still new to the journey.

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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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New post 17 Mar 2015, 06:27
braveally wrote:
Bunuel wrote:
SOLUTION

A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44

Since we need to find only an approximate value and the answer choices are quite widespread, then use:

80% instead of 82% (notice that this approximation gives the bigger tank capacity);
140 billion gallons instead of 138 billion gallons (notice that this approximation also gives the bigger tank capacity);
130 billion gallons instead of 124 billion gallons;.

Notice that the third approximation balances the first two a little bit.

So, we'll have that: \(capacity*0.8=140\) --> \(capacity=\frac{140}{0.8}=175\).

Hence, the amount of water the reservoirs were short of total capacity prior to the storm was approximately \(175-130=45\) billion gallons.

Answer: E.

This is my first post on a question, but this question makes me feel really ignorant. I understand most of the concept for finding the answer, but my general math is not strong. When I see \((140/0.8)\), I feel like that is starting to get math heavy and don't have the skills to handle that in my head. Perhaps there is a concept you can point me too to help manipulate such a fraction in my head or another solution not calculation intensive?
I feel just as ignorant when I see \(138/82%\), otherwise I get how to solve the problem. Please forgive my ignorance, still new to the journey.


There are several ways:

\(\frac{140}{0.8}=\frac{1400}{8}= 175\);

\(\frac{140}{0.8}=\frac{140}{(\frac{4}{5})}= 140*\frac{5}{4}=175\).
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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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New post 17 Mar 2015, 07:05
That clears it up, thanks Bunuel. Recognizing 0.8 as 4/5 is a lot easier for me to handle this question.

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A rainstorm increased the amount of water stored in State J [#permalink]

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New post 02 May 2016, 03:35
The question says 138 is the 82% of the total capacity of reservoir.

for simplifications -
I took 138 as 140 and 82% as 83.33%(which as a fraction is 5/6).

Now you can do the easy calculations -

5/6 of the reservoir is 140 gallon
then whole capacity (1) of the reservoir will be 140*6/5 = 168 gallon

Now we are asked how many gallon was short prior to the storm -
168 - 124 = 44.
pretty easy ;) right!?

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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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New post 02 May 2016, 06:14
Bunuel wrote:
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44

Practice Questions
Question: 6
Page: 152
Difficulty: 600


Solution:

We are given that the water increased from 124 billion gallons to 138 billion gallons. We also know that 138 billion gallons is 82% of the total capacity. Let’s translate this information into an equation, where T = total capacity. We translate the sentence "138 billion gallons is 82% of total capacity" as 138 = (0.82)T, remembering that "is" means "equals" and "of" means "multiply."

However, we are told to APPROXIMATE. So, instead of using the equation 0.82T = 138, we can instead use 0.8T = 136. Note that I chose 136 because I know that it is divisible by 8, but you could just as easily use 138 and ignore the decimal values. Now we need to solve for T.

T = 136/0.8
T = 1360/8
T = 170

The total capacity is approximately 170 billion gallons. It follows that the reservoirs were approximately 170 – 124 = 46 billion gallons short of capacity prior to the storm.

From our approximated answer, we see that answer choice E (44) is closest.

Answer E.
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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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New post 30 May 2016, 20:03
Assume the total capacity = 100x billion gallons
Given that 138 billion gallons = 82x

x = 138/82 = 1.68
Total water = 168 billion gallons
Initial water level was 168 - 124 = 44 billion gallons short of the capacity

Correct Option: E

We can also approximate the values to get the answer approximately.
x = 138/82 = 140/80 = 1.7 (Note that since we have increased the numerator and decreased the denominator, the final value will be larger)
Total water = 170 billion gallons
Difference = 170 - 124 = 46 billion gallons.
Only option E is the closest.

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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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New post 30 May 2016, 20:50
Bunuel wrote:
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44



so 82 % of total capacity = 138 gallons.

so Total capacity = (138 / 0.82)

Shortage = (138/0.82) - 124 = 172.5 - 124 = 48.

Answer : E

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Re: A rainstorm increased the amount of water stored in State J [#permalink]

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New post 30 May 2016, 20:50
Bunuel wrote:
A rainstorm increased the amount of water stored in State J reservoirs from 124 billion gallons to 138 billion gallons. If the storm increased the amount of water in the reservoirs to 82 percent of total capacity, approximately how many billion gallons of water were the reservoirs short of total capacity prior to the storm?

(A) 9
(B) 14
(C) 25
(D) 30
(E) 44



so 82 % of total capacity = 138 gallons.

so Total capacity = (138 / 0.82)

Shortage = (138/0.82) - 124 = 172.5 - 124 = 48.

Answer : E

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